Finite Group Databasebeta

← C2×#22613061 #33245698

Subgroups — C2×#22613061 #33245698

Order 18688.

3094 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556575C211yesmaximal, characteristic
2#22613061C2116yesmaximal, direct product factor
3C2×#17988487C211yesmaximal, characteristic
4C2×#17988480C211yesmaximal, characteristic, complemented
5C2×#17988479C211yesmaximal, characteristic, complemented
6C2×#17988477C211yesmaximal, characteristic, complemented
7C2×#17988472C211yesmaximal, characteristic, complemented
8C2×#17988470C211yesmaximal, characteristic, complemented
9C2×#17988463C211yesmaximal, characteristic
10C2×C4⋊C4×Dic73C211yesmaximal, characteristic, complemented
11C2×C4×C4⋊Dic73C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
14C2×C4×#11924005C211yesmaximal, characteristic, complemented
15C2×#17988434C211yesmaximal, characteristic, complemented
16C2×#388×C73C211yesmaximal, characteristic, complemented
17C23×C22⋊D73C2211yescharacteristic
18C24×Dic73C2211yescharacteristic
19C23×C4×D73C2211yescharacteristic
20C2×#14556575C4116yescomplemented
21C2×#14556575C2218yes—
22C22×C4⋊Dic73C2211yescharacteristic
23C22×C4⋊Dic73C2211yescharacteristic
24C22×C4⋊Dic73C2211yescharacteristic
25C22×#11924007C2211yescharacteristic
26C22×C22⋊Dic73C2211yescharacteristic
27C22×C22⋊Dic73C2211yescharacteristic
28C22×#11924005C2211yescharacteristic
29C22×#11924005C2211yescharacteristic
30C22×#11924005C2211yescharacteristic
31C22×#11924005C2211yescharacteristic
32C22×#11924005C2211yescharacteristic
33C22×C4×Dic73C2211yescharacteristic
34C22×C4×Dic73C2211yescharacteristic
35C22×C4×Dic73C2211yescharacteristic
36C22×C4×Dic73C2211yescharacteristic
37C22×C4×Dic73C2211yescharacteristic
38C22×C4×Dic73C2211yescharacteristic
39#17988487C2218yes—
40#17988480C2218yescomplemented
41#17988479C2218yescomplemented
42#17988477C2218yescomplemented
43#17988472C2218yescomplemented
44#17988470C2218yescomplemented
45#17988463C2218yes—
46C4⋊C4×Dic73C2218yescomplemented
47C4×C4⋊Dic73C2218yescomplemented
48C22⋊C4×Dic73C2218yescomplemented
49C22⋊C4×Dic73C2218yescomplemented
50C4×#11924005C2218yescomplemented
51#17988434C2218yescomplemented
52C2×#14556498C2211yescharacteristic
53C2×#14556498C2211yescharacteristic
54C2×#14556498C2211yescharacteristic
55C2×#14556498C2211yescharacteristic
56C2×#14556498C2211yescharacteristic
57C2×#14556498C2211yescharacteristic
58C2×#14556498C2211yescharacteristic
59C2×#14556498C2211yescharacteristic
60C22×C4⋊C4×C73C2211yescharacteristic
61C22×C22⋊C4×C73C2211yescharacteristic
62C22×C22⋊C4×C73C2211yescharacteristic
63C22×C22⋊C4×C73C2211yescharacteristic
64C22×C42×C73C2211yescharacteristic
65#388×C73C2218yescomplemented
66C2×#95×C73C2211yescharacteristic
67C2×#95×C73C2211yescharacteristic
68C24×D73C2311yescharacteristic
69C22×C22⋊D73—42no—
70C22×C22⋊D73—42no—
71C22×C22⋊D73C2×C418yes—
72C22×C22⋊D73C2314yes—
73C23×Dic73—42no—
74C23×Dic73—42no—
75C23×Dic73C2×C418yescomplemented
76C23×Dic73C2311yescharacteristic
77C23×Dic73C2311yescharacteristic
78C23×Dic73C2311yescharacteristic
79C23×Dic73C2311yescharacteristic
80C23×Dic73C2311yescharacteristic
81C23×Dic73C2311yescharacteristic
82C23×Dic73C2311yescharacteristic
83C23×Dic73C2314yes—
84C22×C4×D73—24no—
85C22×C4×D73—24no—
86C22×C4×D73—42no—
87C22×C4×D73C2314yes—
88#14556575C2×C4164yescomplemented
89C2×C4⋊Dic73—24no—
90C2×C4⋊Dic73C2×C418yescomplemented
91C2×C4⋊Dic73C2×C418yescomplemented
92C2×C4⋊Dic73C2314yes—
93C2×C4⋊Dic73C2314yes—
94C2×C4⋊Dic73C2314yes—
95C2×#11924007—42no—
96C2×#11924007C2314yes—
97C2×C22⋊Dic73—24no—
98C2×C22⋊Dic73—24no—
99C2×C22⋊Dic73C2314yes—
100C2×C22⋊Dic73C2314yes—
101C2×#11924005—24no—
102C2×#11924005—24no—
103C2×#11924005—42no—
104C2×#11924005C2×C418yes—
105C2×#11924005C2×C418yes—
106C2×#11924005C2314yes—
107C2×#11924005C2314yes—
108C2×#11924005C2314yes—
109C2×#11924005C2314yes—
110C2×#11924005C2314yes—
111C2×C4×Dic73—24no—
112C2×C4×Dic73—42no—
113C2×C4×Dic73—42no—
114C2×C4×Dic73—42no—
115C2×C4×Dic73—42no—
116C2×C4×Dic73—42no—
117C2×C4×Dic73C2314yes—
118C2×C4×Dic73C2314yes—
119C2×C4×Dic73C2314yes—
120C2×C4×Dic73C2314yes—
121C2×C4×Dic73C2314yes—
122C2×C4×Dic73C2314yes—
123#14556498C2314yes—
124#14556498C2314yes—
125#14556498C2314yes—
126#14556498C2314yes—
127#14556498C2314yes—
128#14556498C2314yes—
129#14556498C2314yes—
130#14556498C2314yes—
131C25×C73C2311yescharacteristic
132C23×C4×C73C2311yescharacteristic
133C23×C4×C73C2311yescharacteristic
134C23×C4×C73C2311yescharacteristic
135C23×C4×C73C2311yescharacteristic
136C23×C4×C73C2311yescharacteristic
137C23×C4×C73C2311yescharacteristic
138C2×C4⋊C4×C73—24no—
139C2×C4⋊C4×C73C2314yes—
140C2×C22⋊C4×C73—24no—
141C2×C22⋊C4×C73—24no—
142C2×C22⋊C4×C73C2×C418yescomplemented
143C2×C22⋊C4×C73C2314yes—
144C2×C22⋊C4×C73C2314yes—
145C2×C22⋊C4×C73C2314yes—
146C2×C42×C73—24no—
147C2×C42×C73C2314yes—
148#95×C73C2314yes—
149#95×C73C2314yes—
150C23×D73—22no—
151C23×D73—22no—
152C23×D73—22no—
153C23×D73—22no—
154C23×D73—22no—
155C23×D73—22no—
156C23×D73C22×C414yes—
157C23×D73C2412yes—
158C2×C22⋊D73—416no—
159C2×C22⋊D73—44no—
160C2×C22⋊D73—44no—
161C2×C22⋊D73C22×C4116yes—
162C22×Dic73—22no—
163C22×Dic73—22no—
164C22×Dic73—22no—
165C22×Dic73—22no—
166C22×Dic73—22no—
167C22×Dic73—22no—
168C22×Dic73—22no—
169C22×Dic73—22no—
170C22×Dic73—22no—
171C22×Dic73—22no—
172C22×Dic73—22no—
173C22×Dic73—22no—
174C22×Dic73—22no—
175C22×Dic73—22no—
176C22×Dic73—22no—
177C22×Dic73—22no—
178C22×Dic73—416no—
179C22×Dic73—44no—
180C22×Dic73—44no—
181C22×Dic73C22×C414yes—
182C22×Dic73C22×C414yes—
183C22×Dic73C22×C414yes—
184C22×Dic73C22×C4116yescomplemented
185C22×Dic73#4114yes—
186C22×Dic73#4114yes—
187C22×Dic73C2412yes—
188C22×Dic73C2412yes—
189C22×Dic73C2412yes—
190C22×Dic73C2412yes—
191C22×Dic73C2412yes—
192C22×Dic73C2412yes—
193C22×Dic73C2412yes—
194C2×C4×D73—28no—
195C2×C4×D73—28no—
196C2×C4×D73—44no—
197C2×C4×D73—416no—
198C4⋊Dic73—28no—
199C4⋊Dic73C22×C4116yescomplemented
200C4⋊Dic73C22×C4116yescomplemented
201#11924007—44no—
202C22⋊Dic73—28no—
203C22⋊Dic73—28no—
204#11924005—28no—
205#11924005—28no—
206#11924005—44no—
207#11924005C22×C4116yes—
208#11924005C22×C4116yes—
209C4×Dic73—28no—
210C4×Dic73—44no—
211C4×Dic73—44no—
212C4×Dic73—44no—
213C4×Dic73—44no—
214C4×Dic73—44no—
215C24×C73—22no—
216C24×C73—22no—
217C24×C73—22no—
218C24×C73—22no—
219C24×C73—22no—
220C24×C73—22no—
221C24×C73C22×C414yes—
222C24×C73C2412yes—
223C24×C73C2411yescharacteristic
224C22×C4×C73—22no—
225C22×C4×C73—22no—
226C22×C4×C73—22no—
227C22×C4×C73—22no—
228C22×C4×C73—22no—
229C22×C4×C73—22no—
230C22×C4×C73—22no—
231C22×C4×C73—22no—
232C22×C4×C73—22no—
233C22×C4×C73—22no—
234C22×C4×C73—22no—
235C22×C4×C73—22no—
236C22×C4×C73—22no—
237C22×C4×C73—22no—
238C22×C4×C73C22×C414yes—
239C22×C4×C73C22×C414yes—
240C22×C4×C73#4114yes—
241C22×C4×C73#4114yes—
242C22×C4×C73C2412yes—
243C22×C4×C73C2412yes—
244C22×C4×C73C2412yes—
245C22×C4×C73C2412yes—
246C22×C4×C73C2412yes—
247C22×C4×C73C2412yes—
248C4⋊C4×C73—28no—
249C22⋊C4×C73—28no—
250C22⋊C4×C73—28no—
251C22⋊C4×C73C22×C4116yescomplemented
252C42×C73—28no—
253C23×C73—28no—
254C23×C73—28no—
255C23×C73—28no—
256C23×C73—22no—
257C23×C73—22no—
258C23×C73—22no—
259C23×C73—22no—
260C23×C73—22no—
261C23×C73—22no—
262C23×C73—44no—
263C23×C73—44no—
264C23×C73—44no—
265C23×C73—44no—
266C23×C73C23×C414yes—
267C23×C73C23×C412yes—
268C23×C73C2×#4112yes—
269C23×C73C2×#4112yes—
270C23×C73C2×#4112yes—
271C23×C73C2×#4112yes—
272C23×C73H(5,𝔽2)12yes—
273C23×C73H(5,𝔽2)12yes—
274C23×C73C2511yescharacteristic
275C22×D73—28no—
276C22×D73—28no—
277C22×D73—28no—
278C22×D73—22no—
279C22×D73—22no—
280C22×D73—22no—
281C22×D73—22no—
282C22×D73—22no—
283C22×D73—22no—
284C22×D73—44no—
285C22×D73—44no—
286C22×D73—44no—
287C22×D73—44no—
288C22×D73C23×C414yes—
289C2×C4×C73—28no—
290C2×C4×C73—28no—
291C2×C4×C73—28no—
292C2×C4×C73—28no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—22no—
298C2×C4×C73—22no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—22no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—22no—
305C2×C4×C73—22no—
306C2×C4×C73—22no—
307C2×C4×C73—44no—
308C2×C4×C73—44no—
309C2×C4×C73C23×C414yes—
310C2×C4×C73C23×C414yes—
311C2×C4×C73C2×#4114yes—
312C2×C4×C73C2×#4114yes—
313C22⋊D73—416no—
314C2×Dic73—28no—
315C2×Dic73—28no—
316C2×Dic73—28no—
317C2×Dic73—28no—
318C2×Dic73—28no—
319C2×Dic73—22no—
320C2×Dic73—22no—
321C2×Dic73—22no—
322C2×Dic73—22no—
323C2×Dic73—22no—
324C2×Dic73—22no—
325C2×Dic73—22no—
326C2×Dic73—22no—
327C2×Dic73—22no—
328C2×Dic73—22no—
329C2×Dic73—22no—
330C2×Dic73—22no—
331C2×Dic73—22no—
332C2×Dic73—22no—
333C2×Dic73—22no—
334C2×Dic73—22no—
335C2×Dic73—416no—
336C2×Dic73—44no—
337C2×Dic73—44no—
338C2×Dic73C23×C414yes—
339C2×Dic73C23×C414yes—
340C2×Dic73C23×C414yes—
341C2×Dic73C2×#4114yes—
342C2×Dic73C2×#4114yes—
343C4×D73—416no—
344C22×C73—24no—
345C22×C73—24no—
346C22×C73—24no—
347C22×C73—416no—
348C22×C73—42no—
349C22×C73—42no—
350C22×C73—42no—
351C22×C73—42no—
352C22×C73C4×#4114yes—
353C22×C73C4×#4114yes—
354C22×C73#51814yes—
355C22×C73#55114yes—
356C22×C73#55314yes—
357C22×C73#55314yes—
358C22×C73#55914yes—
359C22×C73C24×C411yescharacteristic
360C22×C73C22×#4111yescharacteristic
361C22×C73C22×#4111yescharacteristic
362C22×C73C22×#4111yescharacteristic
363C22×C73C22×#4111yescharacteristic
364C22×C73C2×H(5,𝔽2)11yescharacteristic
365C22×C73C2×H(5,𝔽2)11yescharacteristic
366C2×D73—24no—
367C2×D73—24no—
368C2×D73—24no—
369C2×D73—416no—
370C2×D73—42no—
371C2×D73—42no—
372C2×D73—42no—
373C2×D73—42no—
374C4×C73—24no—
375C4×C73—24no—
376C4×C73—24no—
377C4×C73—24no—
378C4×C73—42no—
379C4×C73—42no—
380Dic73—24no—
381Dic73—24no—
382Dic73—24no—
383Dic73—24no—
384Dic73—24no—
385Dic73—42no—
386Dic73—42no—
387C2×#2374—731nomaximal, Sylow
388C2×C73—44no—
389C2×C73#237418yescomplemented
390C2×C73C2×C4×#4111yescharacteristic
391C2×C73C2×C4×#4111yescharacteristic
392C2×C73C2×#51811yescharacteristic
393C2×C73C2×#55111yescharacteristic
394C2×C73C2×#55311yescharacteristic
395C2×C73C2×#55311yescharacteristic
396C2×C73C2×#55911yescharacteristic
397D73—44no—
398C22×#123—731no—
399#2374—7316no—
400C2×#390—731no—
401C2×#388—731no—
402C2×#388—731no—
403C2×#388—731no—
404C2×#388D7311yescharacteristic, complemented
405C2×#387—731no—
406C2×#387—731no—
407C2×#386—731no—
408C2×C4×C4⋊C4—731no—
409C2×C4×C4⋊C4—731no—
410C2×C4×C22⋊C4—731no—
411C2×C4×C22⋊C4—731no—
412C2×C4×C22⋊C4—731no—
413C2×C4×C22⋊C4—731no—
414C73C2×#237411yescharacteristic, complemented, Sylow
415C23×D4—731no—
416C24×C4—731no—
417C24×C4—731no—
418C2×#123—7316no—
419C2×#123—738no—
420C22×C4⋊C4—731no—
421C22×C4⋊C4—731no—
422C22×C4⋊C4—731no—
423C22×C4⋊C4—731no—
424C22×C4⋊C4C2×D7311yescharacteristic
425C22×C22⋊C4—731no—
426C22×C22⋊C4—731no—
427C22×C22⋊C4—731no—
428C22×C22⋊C4—731no—
429C22×C22⋊C4—731no—
430C22×C22⋊C4—731no—
431C22×C22⋊C4—731no—
432C22×C22⋊C4C2×D7311yescharacteristic
433C22×C22⋊C4C2×D7311yescharacteristic
434C22×C22⋊C4C2×D7311yescharacteristic
435C22×C42—731no—
436C22×C42—731no—
437C22×C42—731no—
438C22×C42—731no—
439C22×C42—731no—
440C22×C42—731no—
441C22×C42C2×D7311yescharacteristic
442#390—738no—
443#388—738no—
444#388—738no—
445#388—738no—
446#388C2×D7318yescomplemented
447#387—738no—
448#387—738no—
449#386—738no—
450C4×C4⋊C4—738no—
451C4×C4⋊C4—738no—
452C4×C22⋊C4—738no—
453C4×C22⋊C4—738no—
454C4×C22⋊C4—738no—
455C4×C22⋊C4—738no—
456C2×#95—731no—
457C2×#95—731no—
458C2×#95—731no—
459C2×#95—731no—
460C2×#95—731no—
461C2×#95—731no—
462C2×#95—731no—
463C2×#95—731no—
464C2×#95C2×D7311yescharacteristic
465C2×#95C2×D7311yescharacteristic
466C25—731no—
467C25C22×D7311yescharacteristic
468C22×D4—2922no—
469C22×D4—2922no—
470C22×D4—738no—
471C22×D4—734no—
472C23×C4—2922no—
473C23×C4—2922no—
474C23×C4—2922no—
475C23×C4—738no—
476C23×C4—734no—
477C23×C4—734no—
478C23×C4—731no—
479C23×C4—731no—
480C23×C4—731no—
481C23×C4—731no—
482C23×C4—731no—
483C23×C4—731no—
484C23×C4—731no—
485C23×C4—1464no—
486C23×C4—1464no—
487C23×C4C22×D7311yescharacteristic
488C23×C4C22×D7311yescharacteristic
489C23×C4C22×D7311yescharacteristic
490C23×C4C22×D7311yescharacteristic
491C23×C4C22×D7311yescharacteristic
492C23×C4C22×D7311yescharacteristic
493#123—7364no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—2922no—
496C2×C4⋊C4—734no—
497C2×C4⋊C4—738no—
498C2×C4⋊C4—738no—
499C2×C4⋊C4—734no—
500C2×C4⋊C4—734no—
501C2×C4⋊C4—734no—
502C2×C4⋊C4—1464no—
503C2×C4⋊C4C22×D7314yes—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—2922no—
507C2×C22⋊C4—734no—
508C2×C22⋊C4—738no—
509C2×C22⋊C4—738no—
510C2×C22⋊C4—734no—
511C2×C22⋊C4—734no—
512C2×C22⋊C4—734no—
513C2×C22⋊C4—734no—
514C2×C22⋊C4—734no—
515C2×C22⋊C4—734no—
516C2×C22⋊C4—1464no—
517C2×C22⋊C4—1464no—
518C2×C22⋊C4—1464no—
519C2×C22⋊C4—1464no—
520C2×C22⋊C4C4×D7318yescomplemented
521C2×C22⋊C4C22×D7314yes—
522C2×C22⋊C4C22×D7314yes—
523C2×C22⋊C4C22×D7314yes—
524C2×C42—24no—
525C2×C42—2922no—
526C2×C42—2922no—
527C2×C42—2922no—
528C2×C42—2922no—
529C2×C42—2922no—
530C2×C42—734no—
531C2×C42—734no—
532C2×C42—734no—
533C2×C42—734no—
534C2×C42—734no—
535C2×C42—734no—
536C2×C42—1464no—
537C2×C42C22×D7314yes—
538#95—734no—
539#95—734no—
540#95—734no—
541#95—734no—
542#95—734no—
543#95—734no—
544#95—734no—
545#95—734no—
546#95C22×D7314yes—
547#95C22×D7314yes—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—734no—
555C24—732no—
556C24—1462no—
557C24—1462no—
558C24—1462no—
559C24—1462no—
560C24—1462no—
561C24—1462no—
562C24C2×C4×D7314yes—
563C24C23×D7312yes—
564C24C23×D7311yescharacteristic
565C2×D4—2924no—
566C2×D4—2924no—
567C2×D4—29216no—
568C2×D4—7316no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—29216no—
584C22×C4—2924no—
585C22×C4—2924no—
586C22×C4—2924no—
587C22×C4—29216no—
588C22×C4—7316no—
589C22×C4—734no—
590C22×C4—734no—
591C22×C4—734no—
592C22×C4—734no—
593C22×C4—734no—
594C22×C4—732no—
595C22×C4—732no—
596C22×C4—732no—
597C22×C4—732no—
598C22×C4—732no—
599C22×C4—732no—
600C22×C4—732no—
601C22×C4—1468no—
602C22×C4—1462no—
603C22×C4—1462no—
604C22×C4—1462no—
605C22×C4—1462no—
606C22×C4—1462no—
607C22×C4—1462no—
608C22×C4—1468no—
609C22×C4—1462no—
610C22×C4—1462no—
611C22×C4—1462no—
612C22×C4—1462no—
613C22×C4—1462no—
614C22×C4—1462no—
615C22×C4—1462no—
616C22×C4—1462no—
617C22×C4—1462no—
618C22×C4—1462no—
619C22×C4C2×C4×D7314yes—
620C22×C4C2×C4×D7314yes—
621C22×C4#1192402714yes—
622C22×C4#1192402714yes—
623C22×C4C23×D7312yes—
624C22×C4C23×D7312yes—
625C22×C4C23×D7312yes—
626C22×C4C23×D7312yes—
627C22×C4C23×D7312yes—
628C22×C4C23×D7312yes—
629C4⋊C4—28no—
630C4⋊C4—2924no—
631C4⋊C4—7316no—
632C4⋊C4—7316no—
633C4⋊C4—1468no—
634C22⋊C4—28no—
635C22⋊C4—28no—
636C22⋊C4—2924no—
637C22⋊C4—7316no—
638C22⋊C4—7316no—
639C22⋊C4—1468no—
640C22⋊C4—1468no—
641C22⋊C4—1468no—
642C22⋊C4—1468no—
643C22⋊C4C2×C4×D73116yescomplemented
644C42—28no—
645C42—2924no—
646C42—2924no—
647C42—2924no—
648C42—2924no—
649C42—2924no—
650C42—1468no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—2924no—
665C23—2924no—
666C23—2924no—
667C23—2924no—
668C23—734no—
669C23—1462no—
670C23—1462no—
671C23—1462no—
672C23—1462no—
673C23—1462no—
674C23—1462no—
675C23—1468no—
676C23—1468no—
677C23—1468no—
678C23C22×C4×D7314yes—
679C23C22×C4×D7312yes—
680C23#41×D7312yes—
681C23#41×D7312yes—
682C23C2×#1192402712yes—
683C23C2×#1192402712yes—
684C23#1455663712yes—
685C23#1455663712yes—
686C23C24×D7311yescharacteristic
687D4—29216no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—28no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—29216no—
709C2×C4—2924no—
710C2×C4—2924no—
711C2×C4—29216no—
712C2×C4—734no—
713C2×C4—734no—
714C2×C4—734no—
715C2×C4—734no—
716C2×C4—734no—
717C2×C4—1462no—
718C2×C4—1462no—
719C2×C4—1462no—
720C2×C4—1462no—
721C2×C4—1462no—
722C2×C4—1462no—
723C2×C4—1462no—
724C2×C4—1462no—
725C2×C4—1462no—
726C2×C4—1462no—
727C2×C4—1462no—
728C2×C4—1462no—
729C2×C4—1462no—
730C2×C4—1462no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1468no—
734C2×C4—1468no—
735C2×C4—1468no—
736C2×C4—1468no—
737C2×C4—1468no—
738C2×C4C22×C4×D7314yes—
739C2×C4C22×C4×D7314yes—
740C2×C4C2×#1192402714yes—
741C2×C4C2×#1192402714yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—42no—
746C22—416no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—2922no—
751C22—29216no—
752C22—2922no—
753C22—2922no—
754C22—2922no—
755C22—1464no—
756C22—1464no—
757C22—1464no—
758C22C4×#1192402714yes—
759C22C4×#1192402714yes—
760C22#1798906114yes—
761C22#1798926014yes—
762C22#1798928814yes—
763C22#1798928914yes—
764C22#1798931914yes—
765C22C23×C4×D7311yescharacteristic
766C22C2×#41×D7311yescharacteristic
767C22C2×#41×D7311yescharacteristic
768C22C22×#1192402711yescharacteristic
769C22C22×#1192402711yescharacteristic
770C22C2×#1455663711yescharacteristic
771C22C2×#1455663711yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—2922no—
779C4—2922no—
780C4—1464no—
781C4—1464no—
782C4—1464no—
783C4—1464no—
784C4—1464no—
785C2—44no—
786C2—2924no—
787C2#2261306118yesdirect product factor
788C2C2×C4×#1192402711yescharacteristic
789C2C2×C4×#1192402711yescharacteristic
790C2C2×#1798906111yescharacteristic
791C2C2×#1798926011yescharacteristic
792C2C2×#1798928811yescharacteristic
793C2C2×#1798928911yescharacteristic
794C2C2×#1798931911yescharacteristic
subgroupG/H
centerC24C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC2×#388×C73C2
socleC24×C73C24
prime radicalC23×C22⋊D73C22
cosocleC23×C73C25
hypercenterC2×#388D73
hypocenterC73C2×#2374
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×#388

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #22613061C2direct (N × H)
4. C2×#17988480C2semidirect
5. C2×#17988479C2semidirect
6. C2×#17988477C2semidirect
7. C2×#17988472C2semidirect
8. C2×#17988470C2semidirect
10. C2×C4⋊C4×Dic73C2semidirect
11. C2×C4×C4⋊Dic73C2semidirect
12. C2×C22⋊C4×Dic73C2semidirect
13. C2×C22⋊C4×Dic73C2semidirect
14. C2×C4×#11924005C2semidirect
15. C2×#17988434C2semidirect
16. C2×#388×C73C2semidirect
20. C2×#14556575C4semidirect
40. #17988480C22semidirect
41. #17988479C22semidirect
42. #17988477C22semidirect
43. #17988472C22semidirect
44. #17988470C22semidirect
46. C4⋊C4×Dic73C22semidirect
47. C4×C4⋊Dic73C22semidirect
48. C22⋊C4×Dic73C22semidirect
49. C22⋊C4×Dic73C22semidirect
50. C4×#11924005C22semidirect
51. #17988434C22semidirect
65. #388×C73C22semidirect
75. C23×Dic73C2×C4semidirect
88. #14556575C2×C4semidirect
90. C2×C4⋊Dic73C2×C4semidirect
91. C2×C4⋊Dic73C2×C4semidirect
142. C2×C22⋊C4×C73C2×C4semidirect
184. C22×Dic73C22×C4semidirect
199. C4⋊Dic73C22×C4semidirect
200. C4⋊Dic73C22×C4semidirect
251. C22⋊C4×C73C22×C4semidirect
389. C2×C73#2374semidirect
404. C2×#388D73semidirect
414. C73C2×#2374semidirect
446. #388C2×D73semidirect
520. C2×C22⋊C4C4×D73semidirect
643. C22⋊C4C2×C4×D73semidirect
787. C2#22613061direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#145565752
#226130612
C2×#179884872
C2×#179884802
C2×#179884792
C2×#179884772
C2×#179884722
C2×#179884702
C2×#179884632
C2×C4⋊C4×Dic732
C2×C4×C4⋊Dic732
C2×C22⋊C4×Dic732
C2×C4×#119240052
C2×#179884342
C2×#388×C732
C2×#237473